On split Lie triple systems
type: Item
instance of: scholarly article
title: On split Lie triple systems
zbMATH Open document ID: 1193.17003
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2009-09-14T00:00:00Z
review text: A Lie triple system \(T\) is said to be split if there is a maximal abelian diagonalizable subalgebra \(H\) of its Lie algebra of inner derivations. In this situation, the triple system splits as \(T=T_0\oplus(\oplus_{\alpha\in\Lambda}T_\alpha)\), for a set \(\Lambda\) of nonzero linear functions on \(H\), where \(T_\alpha=\{ x\in T: d(x)=\alpha(d)x\;\forall d\in H\}\). The paper under review is devoted to study these systems under some extra technical conditions on the root system \(\Lambda\), which guarantee that any such Lie triple system is a direct sum of simple ones. The key tool is a notion of connection of roots in this setting.
reviewed by: Alberto Elduque
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 5603918
zbMATH Keywords: Lie triple system
zbMATH Keywords: split
zbMATH Keywords: root system
zbMATH Keywords: connection
zbMATH Keywords: simple
author: Antonio J. Calderón Martín
MaRDI profile type: Publication
full work available at URL: s12044-009-0017-0
OpenAlex ID: W2027059042
cites work: On split Lie algebras with symmetric root systems
cites work: On integrable roots in split Lie triple systems
cites work: On Locally Finite Split Lie Triple Systems
cites work: Dynkin diagrams for Lie triple systems
cites work: A Structure Theory of Lie Triple Systems
cites work: Integrable roots in split graded Lie algebras
cites work: The structure of locally finite split Lie algebras
DOI: 10.1007/S12044-009-0017-0
description: scientific article; zbMATH DE number 5603918